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Approach regions for the square root of the Poisson kernel and bounded functions

Published online by Cambridge University Press:  17 April 2009

P. Sjögren
P. Sjögren
Affiliation:
Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 GöteborgSweden email: peters@math.chalmers.se
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If the Poisson kernel of the unit disc is replaced by its square root, it is known that normalised Poisson integrals of Lp boundary functions converge almost everywhere at the boundary, along approach regions wider than the ordinary non-tangential cones. The sharp approach region, defined by means of a monotone function, increases with p. We make this picture complete by determining along which approach regions one has almost everywhere convergence for L∞ boundary functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 521 - 527
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bellow, A. and Jones, R. L., ‘A Banach principle for L ∞’,Adv. Math. 120 (1996), 155–172.CrossRefGoogle Scholar
[2]Rönning, J.-O., ‘Convergence for square roots of the Poisson kernel in weakly tangential regions’, Math. Scand. (to appear).Google Scholar
[3]Rönning, J.-O., ‘A convergence result for square roots of the Poisson kernel in the bidisk’, Preprint 1993–1934. Dept. of Math., Chalmers Univ. of Techn. and Univ. of Göteborg.Google Scholar
[4]Rönning, J.-O., ‘On convergence for the square root of the Poisson kernel in symmetric spaces of rank 1’, Studia Math. (to appear).Google Scholar
[5]Sjögren, P., ‘Une remarque sur la convergence des fonctions propres du Laplacien à valeur propre critique’, in Théorie du Potentiel, Proceedings Orsay 1983, Lecture Notes in Mathematics 1096 (Springer-Verlag, 1984), pp. 141–147.Google Scholar
[6]Sjögren, P., ‘Convergence for the square root of the Poisson kernel’, Pacific J. Math. 131 (1988), 361–391.CrossRefGoogle Scholar